Some cells in our bodies can reproduce throughout our lives. Blood cells for example are generated every few days for our whole lives. Some cells loose the ability to reproduce shortly after birth. Brain cells for example cannot reproduce, therefore if you loose cells in the brain they cannot be replaced.
As we get older though, cells that reproduce tend to get a build up of errors in their DNA, this means that they probably don’t reproduce or work properly. This may be one of the ways that we age, by accumulating cells with this damage.